7  Population Mean of a Poisson Random Variable (8.4.3)

Using a sample \(\boldsymbol x\) taken from \(X\sim\mbox{Pois}(\lambda)\), a \((1-\alpha)\cdot100\%\) confidence interval for the mean of the distribution \(\lambda\) can be found as,

\[\begin{equation} \tag{8.57} CI_{1-\frac{\alpha}{2}}(\lambda)=\left[\bar x-z_{1-\frac{\alpha}{2}}\cdot\sqrt{\frac{\bar x}{n}}, \bar x+z_{1-\frac{\alpha}{2}}\cdot\sqrt{\frac{\bar x}{n}} \right] \end{equation}\]

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See Section 8.4.3 of Probability and Statistics with R for examples of using this result and its derivation.